To allow for tractable probabilistic inference with respect to domain sizes, lifted probabilistic inference exploits symmetries in probabilistic graphical models. However, checking whether two factors encode equivalent semantics and hence are exchangeable is computationally expensive. In this paper, we efficiently solve the problem of detecting exchangeable factors in a factor graph. In particular, we introduce the detection of exchangeable factors (DEFT) algorithm, which allows us to drastically reduce the computational effort for checking whether two factors are exchangeable in practice. While previous approaches iterate all $O(n!)$ permutations of a factor's argument list in the worst case (where $n$ is the number of arguments of the factor), we prove that DEFT efficiently identifies restrictions to drastically reduce the number of permutations and validate the efficiency of DEFT in our empirical evaluation.

翻译：为在领域规模上进行可处理的概率推理，提升概率推理利用概率图模型中的对称性。然而，检查两个因子是否编码等价语义从而可交换，在计算上代价高昂。本文高效解决了因子图中可交换因子的检测问题。具体而言，我们提出了可交换因子检测（DEFT）算法，该算法在实践中能大幅减少检查两个因子是否可交换所需的计算量。先前的方法在最坏情况下需遍历因子参数列表的所有 $O(n!)$ 种排列（其中 $n$ 为因子的参数数量），而我们证明 DEFT 能高效识别限制条件，从而大幅减少需考虑的排列数，并通过实证评估验证了 DEFT 的高效性。